Weighted nonlocal Laplacian on interpolation from sparse data

DOI10.1007/s10915-017-0421-zzbMath1381.65007OpenAlexW2604163838MaRDI QIDQ1691417

Wei Zhu, Zuoqiang Shi, Stanley J. Osher

Publication date: 16 January 2018

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-017-0421-z

zbMATH Keywords

numerical resultsimage processingimage inpaintingpoint cloudsemi-supervised learninggraph Laplaciannonlocal methodspoint integral methodweighted nonlocal Laplaciancontinuous interpolation function

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Numerical interpolation (65D05) Multidimensional problems (41A63) Interpolation in approximation theory (41A05)

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Uses Software

• MNIST

Cites Work

• Unnamed Item
• Convergence of the point integral method for Laplace-Beltrami equation on point cloud
• Neighborhood filters and PDE's
• Nonlocal infinity Laplacian equation on graphs with applications in image processing and machine learning
• Nonlocal Operators with Applications to Image Processing
• Nonlocal Linear Image Regularization and Supervised Segmentation
• Harmonic Extension on The Point Cloud
• Low Dimensional Manifold Model for Image Processing
• Point Integral Method for Solving Poisson-Type Equations on Manifolds from Point Clouds with Convergence Guarantees
• A Convergent Point Integral Method for Isotropic Elliptic Equations on a Point Cloud
• A Review of Image Denoising Algorithms, with a New One